1.a^2+2b^2+3c^2+3ab+4ac+5bc2.2x^3-x^2z-4x^2y+2xyz+2xy^2-y^2z要步筹

Question

1.a^2+2b^2+3c^2+3ab+4ac+5bc
2.2x^3-x^2z-4x^2y+2xyz+2xy^2-y^2z
要步筹

Answer 1

a^2+2b^2+3c^2+3ab+4ac+5bc = (a + b + c) (a + 2 b + 3 c)
2x^3-x^2z-4x^2y+2xyz+2xy^2-y^2z =(x - y)^2 (2 x - z)
a^2+2b^2+3c^2+3ab+4ac+5bc
=(a^2+ab+ac)+(2ab+2b^2+2bc)+(3ac+3bc+3c^2)
=a(a+b+c)+2b(a+b+c)+3c(a+b+c)
=(a + b + c) (a + 2 b + 3 c)
2x^3-x^2z-4x^2y+2xyz+2xy^2-y^2z
=(2x^3-4x^2y+2xy^2)-(x^2z-2xyz+y^2z)
=2x(x^2-2xy+y^2)-z(x^2-xy+y^2)
=2x(x-y)^2-z(x-y)^2
=(x-y)^2(2x-z)